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Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations

A Monograph Based on Articles of the Founding Authors, Reproduced in Full

  • Book
  • © 2015

Overview

Authors:
  1. Radomir S. Stankovic

    1. Faculty of Electronic Engineering, Nis, Serbia

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  2. Paul L. Butzer

    1. Lehrstuhl A für Mathematik, RWTH Aachen, Aachen, Germany

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  3. Ferenc Schipp

    1. Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

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  4. William R. Wade

    1. Math. and Computer Science, BIOLA University, La Miranda, USA

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  5. Weiyi Su

    1. Mathematics, Nanjing University, Nanjing, China

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  6. Yasushi Endow

    1. Chuo University, Hachioji-shi, Tokyo, Japan

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  7. Sandor Fridli

    1. Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

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  8. Boris I. Golubov

    1. Technologies (State University), Moscow Institute of Physical, Dolgoprudny, Russia

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  9. Franz Pichler

    1. Johannes Kepler University Linz, Linz, Austria

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  • A unique development of a field by seven founding authors, together with reproductions of some of their basic papers
  • Applications to dyadic differential equations, approximation theory, etc
  • Reviews of former and recent results help the reader to get a fast introduction and a rather complete coverage of the area. A separate chapter with open problems should be useful for further research in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: Atlantis Studies in Mathematics for Engineering and Science (ASMES, volume 13)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Early Work in Gibbs Differentiation in China

    • Weiyi Su
    Pages 1-63

  3. Gibbs-Butzer Calculus and Pseudo-differential Operators on Local Fields

    • Weiyi Su, Qiu Hua
    Pages 65-92

  4. Early Work in Gibbs Differentiation in Soviet Union - SSSR

    • Radomir S. Stanković, Paul L. Butzer
    Pages 93-124

  5. Research in Dyadic Differentiation in Russia

    • Boris I. Golubov, Sergei S. Volosivets
    Pages 125-129

  6. Generalized Derivatives and Integrals on Vilenkin Groups

    • Boris I. Golubov, Sergei S. Volosivets
    Pages 131-143

  7. Calculus on Walsh and Vilenkin Groups

    • György Gát, Rodolfo Toledo
    Pages 145-156

  8. Gibbs Derivatives on Groups

    • Radomir S. Stanković
    Pages 157-168

  9. My Research in Gibbs Derivatives on Finite Groups

    • Radomir S. Stanković
    Pages 169-210

  10. Efficient Computation of Gibbs Derivatives on Finite Abelian Groups

    • Radomir S. Stanković, Dušan Gajić
    Pages 211-276

  11. Gibbs Derivative and Walsh Harmonizable DSP

    • Yasushi Endow
    Pages 277-295

  12. My Involvement in Gibbs Derivatives and Walsh Harmonizable Processes

    • Yasushi Endow
    Pages 297-323

  13. Open Problems in Theory and Applications of Dyadic Derivatives

    • Yasushi Endow, Boris I. Golubov, Weiyi Su, W. X. Zheng, Ushangi Goginava
    Pages 325-332

  14. Back Matter

    Pages 333-360
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Keywords

About this book

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. 


Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible.


The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.

Authors and Affiliations

  • Faculty of Electronic Engineering, Nis, Serbia

    Radomir S. Stankovic

  • Lehrstuhl A für Mathematik, RWTH Aachen, Aachen, Germany

    Paul L. Butzer

  • Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

    Ferenc Schipp, Sandor Fridli

  • Math. and Computer Science, BIOLA University, La Miranda, USA

    William R. Wade

  • Mathematics, Nanjing University, Nanjing, China

    Weiyi Su

  • Chuo University, Hachioji-shi, Tokyo, Japan

    Yasushi Endow

  • Technologies (State University), Moscow Institute of Physical, Dolgoprudny, Russia

    Boris I. Golubov

  • Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

Bibliographic Information

  • Book Title: Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations

  • Book Subtitle: A Monograph Based on Articles of the Founding Authors, Reproduced in Full

  • Authors: Radomir S. Stankovic, Paul L. Butzer, Ferenc Schipp, William R. Wade, Weiyi Su, Yasushi Endow, Sandor Fridli, Boris I. Golubov, … Franz Pichler

  • Series Title: Atlantis Studies in Mathematics for Engineering and Science

  • DOI: https://doi.org/10.2991/978-94-6239-163-5

  • Publisher: Atlantis Press Paris

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Atlantis Press and the author(s) 2015

  • Hardcover ISBN: 978-94-6239-162-8Published: 08 January 2016

  • eBook ISBN: 978-94-6239-163-5Published: 29 December 2015

  • Series ISSN: 1875-7642

  • Series E-ISSN: 2467-9631

  • Edition Number: 1

  • Number of Pages: XVIII, 360

  • Number of Illustrations: 9 b/w illustrations

  • Topics: Abstract Harmonic Analysis, Math Applications in Computer Science

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